Use what equation? This is the crucial part!
You can rewrite this sum as
[tex]\frac{1}{n} \sum_{i=0}^n (e^{1/n})^i[/tex]
That's a geometric series with "common ratio" e1/n: its sum is
[tex]\frac{1}{n}\frac{1- e^{(n+1)/n}}{1- e^{1/n}}[/tex]